[QUOTE=foolsguinea]
Klemperer Rosettes are the way to go. Run four moderately large (about 10-20 Earth masses) planets at 12:00, 3:00, 6:00, & 9:00. These can have habitable moons & companions (maybe even Earth-type planets in their outer equilibrium points). To keep the Rosette stable, run class M planets at 1:30, 4:30, 7:30, & 10:30.
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Klemperer rosettes are only marginally stable; a slight perturbation will cause them to become unstable rather quickly, and once perturbed they tend to fling off wildly in seemingly random directions; this can be demonstrated with a very simple simulation in Matlab or Mathematica (or in Python or C if you don’t mind writing real code), where even tiny rounding errors in the precision of calculations will quickly cause a non-correcting orbit to spin out. Klemperer’s paper actually described a system of equal numbers of two or more different mass bodies orbiting a common barycenter; the type of rosette described by Larry Niven as the Fleet of Worlds is actually a trivial subset which is stable (although again, only marginally so) by inspection.
Of course, with a central massive body such that M >>> m1, m2, m3,… you could put a number of bodies in the same orbit at 60° intervals such that each fell within the other’s libration points. Such a system may be at least marginally stable, especially if M1>>>M2~M3~…, although over time influences between minor bodies would affect each other’s orbits. You could also place one body in orbit of a second in orbit of a third, such that M3<<M2<<M1, provided that the ratios between them are M1/M2 is very large and M2/M3>25; this is, in fact, exactly what we have with the Sol-Earth-Luna system. Getting the density sufficient to hold onto an atmosphere might be pretty tricky, though. You could also put two worlds in a tidally-locked couplet in orbit of a much larger mass with pretty good long term stability as long as they’re reasonably close together.
As for the number and arrangement of stable planar orbits, we’re not sure, although there are suspicious similarities in the spacing of orbits which have caused many to look for resonances in orbits. We don’t have anything definitive for planets, although there are some pretty clear resonances in the Jovian moons. I wouldn’t plan on spacing too many orbits close together in a habitable zone; planetary collisions are a bad day all around.
[QUOTE=Projammer]
What would be issues with running orbits out of the ecliptic?
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Very tricky; when dealing with out of plane orbits you have to account for orbital behavior in three dimensions; this is generally contrary to long term stability of the orbit, especially if you have one or more large secondary influences (a Jovian or larger planet).
The real solution for maximizing habitable volume is to get away from planets completely. Spherical worlds are remarkably inefficient–remember, they give minimum surface area for volume–and have all manner of difficulty in getting things like seasons and the length of day just right. Rotating toroids or hollow spheres in massive conjunctive orbits seem like a better use of materials. The o.p. is wise to stay away from Ringworlds and Dyson shells, on the other hand; difficult to stabilize and impossible to defend.
Personally, I’d hide away in the ergosphere of a massive rotating black hole with a good book. Making custom worlds seems like an appealing business until you realize that your customers are going to ask for all sorts of obscene and offensively tacky things. I mean, it’s one thing to go a nice bit of fyords, but when they want a planet that is pink and squishy and squeals every time you walk across it, I’d draw the line.
Stranger